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Proof step 103 from proof putarray-addarray-override (previous step)

0 ≤ i0, n→i(# vals) + i ≤ i0, i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0, i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i, i0 < n→i(# vals0), n→i(# vals) + i < n→i(# vals0), i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) < n→i(# vals0) ⊦ vals0[i→n(i0)] = st[r0 -- i0 '], vals0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 96:
n ≤ # vals ⊦ # restn(n, vals) = # vals - n
Proof step 102:
¬ i→n(i) + # vals ≤ # vals0, 0 ≤ i0, n→i(# vals) + i ≤ i0, i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0, i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i, i0 < n→i(# vals0), n→i(# vals) + i < n→i(# vals0), i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) < n→i(# vals0) ⊦ vals0[i→n(i0)] = st[r0 -- i0 '], vals0 = []

Rule argument

[speclemmaarg: n ≤ # vals ,# restn(n, vals) = # vals - n ,[vals, n] → [vals0, i→n(i) + # vals] ,F ,list-del ,javavalues ,rest-len ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ n ≤ m → n→i(m - n) = n→i(m) - n→i(n)], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ i + (j - i) = j], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (vals0, i→n(i) + # vals)]]